Kaczmarz型内线型内联线性,为一致线性系统提供灵活GMRES方法的先决条件 (Kaczmarz-type inner-iteration preconditioned flexible GMRES methods for consistent linear systems)

We propose using greedy and randomized Kaczmarz inner-iterations as preconditioners for the right-preconditioned flexible GMRES method to solve consistent linear systems, with a parameter tuning strategy for adjusting the number of inner iterations and the relaxation parameter. We also present theoretical justifications of the right-preconditioned flexible GMRES for solving consistent linear systems. Numerical experiments on overdetermined and underdetermined linear systems show that the proposed method is superior to the GMRES method preconditioned by NE-SOR inner iterations in terms of total CPU time.

翻译：我们建议使用贪婪和随机化的卡茨马尔兹内部标准作为先决条件,采用正确前提条件的灵活GMRES方法解决一致线性系统,并采用参数调整战略来调整内部迭代和放松参数的数量,我们还提出以正确前提条件的灵活GMRES解决一致线性系统的理论理由,对定额过高和定额不足的线性系统的数值实验表明,拟议的方法优于以NE-SOR内部迭代为先决条件的GMRES方法,在CPU总时间方面,该方法以NE-SOR内部迭代为先决条件。